The equations from the previous sections can be applied directly to systems such as springs.
They can also be applied to model the motion of a pendulum, as follows:

where g is the acceleration due to gravity, l is the length of the wire/rod the mass is attached to and α is the damping constant.
The presence of the sin(θ) term makes the equation unintegrable, however. By only considering
values of θ where |θ| << 1, then sin(θ) ≈ θ. The equation now becomes